We start by defining line graphs, which are graph constructed from an undirected graph \(\mathcal {G}\)  and such that the edges of the graph \(\mathcal {G}\)  become the vertices of the graph \(\mathcal {L}(\mathcal {G})\) . The edges (or edges) of the line graph are constructed based on the connectivity of the original graph, as follows [1]}, [2]}, [3]}, [4]}.It is interesting to note that here there is a mismatch between the original literature in graph theory, starting with the original work of Harary [3]} (1965). The original Line Graph of a digraph did not have any negative values, e.g. if the two edges do not have zero sum, then we assign a value zero.
